feat(cses): a few problems

kattis/18-2-2025/.clang-format

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+BasedOnStyle: Google
+AllowShortBlocksOnASingleLine: false
+AllowShortCaseLabelsOnASingleLine: false
+AllowShortCompoundRequirementOnASingleLine: false
+AllowShortEnumsOnASingleLine: false
+AllowShortFunctionsOnASingleLine: false
+AllowShortIfStatementsOnASingleLine: false
+AllowShortLambdasOnASingleLine: false
+AllowShortLoopsOnASingleLine: false

kattis/18-2-2025/.clangd

@@ -0,0 +1,9 @@
+CompileFlags:
+	Add:
+		- -std=c++23
+		- -Wall
+		- -Wextra
+		- -Wpedantic
+		- -Wshadow
+		- -DLOCAL
+		- -Wno-unknown-pragmas

kattis/18-2-2025/.null-ls_478791_k.py

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+import math
+from scipy.optimize import minimize_scalar
+
+def cable_length(x, L, H1, H2, d, h):
+    # Calculate the height of the cable at point x
+    y = H1 - (H1 - H2) * (x / L)
+    
+    # Ensure the rider is at least h + d meters above the ground
+    if y - d < h:
+        return float('inf')  # Invalid configuration
+    
+    # Calculate the cable length
+    length1 = math.sqrt(x**2 + (H1 - y)**2)
+    length2 = math.sqrt((L - x)**2 + (H2 - y)**2)
+    return length1 + length2
+
+def find_min_max_length(L, H1, H2, d, h):
+    # Find the minimum length
+    res_min = minimize_scalar(lambda x: cable_length(x, L, H1, H2, d, h), bounds=(0, L), method='bounded')
+    min_length = res_min.fun
+    
+    # Find the maximum length
+    res_max = minimize_scalar(lambda x: -cable_length(x, L, H1, H2, d, h), bounds=(0, L), method='bounded')
+    max_length = -res_max.fun
+    
+    return min_length, max_length
+
+# Example usage:
+L = 1000  # Distance between poles
+H1 = 100  # Height of first pole
+H2 = 100  # Height of second pole
+d = 20    # Distance rider hangs below cable
+h = 10   # Minimum height above ground
+
+min_length, max_length = find_min_max_length(L, H1, H2, d, h)
+print(f"Minimum length: {min_length:.6f} meters")
+print(f"Maximum length: {max_length:.6f} meters")

kattis/18-2-2025/compile_flags.txt

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+-std=c++23
+-Wall
+-Wextra
+-Wpedantic
+-Wshadow
+-DLOCAL

kattis/18-2-2025/i.cc

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+#include <bits/stdc++.h>  // {{{
+
+// https://codeforces.com/blog/entry/96344
+
+#pragma GCC optimize("O2,unroll-loops")
+#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
+
+using namespace std;
+
+template <typename T>
+constexpr T MIN = std::numeric_limits<T>::min();
+
+template <typename T>
+constexpr T MAX = std::numeric_limits<T>::max();
+
+template <typename T>
+[[nodiscard]] static T sc(auto&& x) {
+  return static_cast<T>(x);
+}
+
+template <typename T>
+[[nodiscard]] static T sz(auto&& x) {
+  return static_cast<T>(x.size());
+}
+
+#ifdef LOCAL
+#define dbgln(...) prln(...)
+#define dbg(...) pr(...)
+#endif
+
+using ll = long long;
+using ld = long double;
+template <typename T>
+using vec = std::vector<T>;
+template <typename T, size_t N>
+using arr = std::array<T, N>;
+
+#define ff first
+#define ss second
+#define eb emplace_back
+#define pb push_back
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+//  }}}
+
+void solve() {
+  int n;
+  cin >> n;
+  vec<ld> a(n);
+  for (auto& e : a)
+    cin >> e;
+
+  ld ans = 0.0;
+
+  ld prefix = 0;
+  for (int i = 0; i < n; ++i) {
+    prefix += a[i];
+    ans = max(ans, prefix / (i + 1));
+  }
+
+  ld suffix = 0;
+  for (int i = n - 1; i >= 0; --i) {
+    suffix += a[i];
+    ans = max(ans, suffix / (n - i));
+  }
+
+  cout << ans << endl;
+}
+
+int main() {  // {{{
+  cin.tie(nullptr)->sync_with_stdio(false);
+
+  int t = 1;
+  // cin >> t;
+
+  while (t--) {
+    solve();
+  }
+
+  return 0;
+}
+// }}}

kattis/18-2-2025/i.in

@@ -0,0 +1,2 @@
+4
+4 4 4 4

kattis/18-2-2025/i.out

@@ -0,0 +1,4 @@
+4
+
+[code]: 0
+[time]: 11.9913 ms

kattis/18-2-2025/j.cc

@@ -0,0 +1,92 @@
+#include <bits/stdc++.h>  // {{{
+
+// https://codeforces.com/blog/entry/96344
+
+#pragma GCC optimize("O2,unroll-loops")
+#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
+
+using namespace std;
+
+template <typename T>
+constexpr T MIN = std::numeric_limits<T>::min();
+
+template <typename T>
+constexpr T MAX = std::numeric_limits<T>::max();
+
+template <typename T>
+[[nodiscard]] static T sc(auto &&x) {
+  return static_cast<T>(x);
+}
+
+template <typename T>
+[[nodiscard]] static T sz(auto &&x) {
+  return static_cast<T>(x.size());
+}
+
+template <typename... Args>
+void pr(std::format_string<Args...> fmt, Args &&...args) {
+  std::print(fmt, std::forward<Args>(args)...);
+}
+
+template <typename... Args>
+void pr(std::format_string<Args...> fmt) {
+  std::print(fmt);
+}
+
+template <typename... Args>
+void prln(std::format_string<Args...> fmt, Args &&...args) {
+  std::println(fmt, std::forward<Args>(args)...);
+}
+
+template <typename... Args>
+void prln(std::format_string<Args...> fmt) {
+  std::println(fmt);
+}
+
+void prln() {
+  std::println();
+}
+
+void prln(auto const &t) {
+  std::println("{}", t);
+}
+
+#ifdef LOCAL
+#define dbgln(...) prln(...)
+#define dbg(...) pr(...)
+#endif
+
+using ll = long long;
+using ld = long double;
+template <typename T>
+using vec = std::vector<T>;
+template <typename T, size_t N>
+using arr = std::array<T, N>;
+
+#define ff first
+#define ss second
+#define eb emplace_back
+#define pb push_back
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+//  }}}
+
+void solve() {
+  string s;
+  cin >> s;
+
+  int ans = 0;
+
+
+
+  prln("{}", ans);
+}
+
+int main() {  //  {{{
+  cin.tie(nullptr)->sync_with_stdio(false);
+
+  solve();
+
+  return 0;
+}
+//  }}}

kattis/18-2-2025/j.in

@@ -0,0 +1 @@
+thenumberofgoodstringsis

kattis/18-2-2025/j.out

@@ -0,0 +1,4 @@
+0
+
+[code]: 0
+[time]: 11.1344 ms

kattis/18-2-2025/j.py

@@ -0,0 +1,17 @@
+s = input()
+n = len(s)
+last_occurrence = {}
+total = 0
+
+for right in range(n):
+    char = s[right]
+    left = last_occurrence.get(char, -1) + 1
+
+    unique_chars = set()
+    for l in range(right - 1, left - 1, -1):
+        if s[l] not in unique_chars:
+            total += 1
+        unique_chars.add(s[l])
+    last_occurrence[char] = right
+
+print(total)

kattis/18-2-2025/k.cc

@@ -0,0 +1,99 @@
+#include <bits/stdc++.h>  // {{{
+
+// https://codeforces.com/blog/entry/96344
+
+#pragma GCC optimize("O2,unroll-loops")
+#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
+
+using namespace std;
+
+template <typename T>
+constexpr T MIN = std::numeric_limits<T>::min();
+
+template <typename T>
+constexpr T MAX = std::numeric_limits<T>::max();
+
+template <typename T>
+[[nodiscard]] static T sc(auto&& x) {
+  return static_cast<T>(x);
+}
+
+template <typename T>
+[[nodiscard]] static T sz(auto&& x) {
+  return static_cast<T>(x.size());
+}
+
+template <typename... Args>
+void pr(std::format_string<Args...> fmt, Args&&... args) {
+  std::print(fmt, std::forward<Args>(args)...);
+}
+
+template <typename... Args>
+void pr(std::format_string<Args...> fmt) {
+  std::print(fmt);
+}
+
+template <typename... Args>
+void prln(std::format_string<Args...> fmt, Args&&... args) {
+  std::println(fmt, std::forward<Args>(args)...);
+}
+
+template <typename... Args>
+void prln(std::format_string<Args...> fmt) {
+  std::println(fmt);
+}
+
+void prln() {
+  std::println();
+}
+
+void prln(auto const& t) {
+  std::println("{}", t);
+}
+
+#ifdef LOCAL
+#define dbgln(...) prln(...)
+#define dbg(...) pr(...)
+#endif
+
+using ll = long long;
+using ld = long double;
+template <typename T>
+using vec = std::vector<T>;
+template <typename T, size_t N>
+using arr = std::array<T, N>;
+
+#define ff first
+#define ss second
+#define eb emplace_back
+#define pb push_back
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+//  }}}
+
+void solve() {
+  ld w, g, h, r;
+  cin >> w >> g >> h >> r;
+
+  auto dist = [](ld x1, ld y1, ld x2, ld y2) {
+    return sqrtl((y2 - y1) * (y2 - y1) + (x2 - x1) * (x2 - x1));
+  };
+
+  ld x_star = w * (g - r) / (g + h - 2 * r);
+  ld min_dist = dist(0, g, x_star, r) + dist(x_star, r, w, h);
+  printf("%.7LF %.7LF\n", dist(0, g, w, h), min_dist);
+}
+
+int main() {  // {{{
+  cin.tie(nullptr)->sync_with_stdio(false);
+
+  int t = 1;
+  cin >> t;
+
+  while (t--) {
+    solve();
+  }
+
+  return 0;
+}
+// }}}

kattis/18-2-2025/k.in

@@ -0,0 +1,3 @@
+2
+1000 100 100 20
+100 20 30 2

kattis/18-2-2025/k.out

@@ -0,0 +1,5 @@
+1000.0000000 1012.7191121
+100.4987562 110.0727032
+
+[code]: 0
+[time]: 11.523 ms

kattis/18-2-2025/k.py

@@ -0,0 +1,37 @@
+import math
+from scipy.optimize import minimize_scalar
+
+def cable_length(x, L, H1, H2, d, h):
+    # Calculate the height of the cable at point x
+    y = H1 - (H1 - H2) * (x / L)
+    
+    # Ensure the rider is at least h + d meters above the ground
+    if y - d < h:
+        return float('inf')  # Invalid configuration
+    
+    # Calculate the cable length
+    length1 = math.sqrt(x**2 + (H1 - y)**2)
+    length2 = math.sqrt((L - x)**2 + (H2 - y)**2)
+    return length1 + length2
+
+def find_min_max_length(L, H1, H2, d, h):
+    # Find the minimum length
+    res_min = minimize_scalar(lambda x: cable_length(x, L, H1, H2, d, h), bounds=(0, L), method='bounded')
+    min_length = res_min.fun
+    
+    # Find the maximum length
+    res_max = minimize_scalar(lambda x: -cable_length(x, L, H1, H2, d, h), bounds=(0, L), method='bounded')
+    max_length = -res_max.fun
+    
+    return min_length, max_length
+
+# Example usage:
+L = 1000  # Distance between poles
+H1 = 100  # Height of first pole
+H2 = 100  # Height of second pole
+d = 20    # Distance rider hangs below cable
+h = 20   # Minimum height above ground
+
+min_length, max_length = find_min_max_length(L, H1, H2, d, h)
+print(f"Minimum length: {min_length:.6f} meters")
+print(f"Maximum length: {max_length:.6f} meters")